Josephson Effects in Superconductors Advanced Lab Course Experiment #16 at the Walther–Meißner–Institut Physik-Department Technische Universit¨atM¨unchen March 27, 2017 Contents 1 Safety4 1.1 Handling of liquid helium.........................4 1.2 Electronic measurement equipment....................5 1.3 Food and drinks...............................6 2 Introduction7 2.1 Superconductivity..............................7 2.2 Josephson effects.............................. 11 2.2.1 Theory................................ 11 2.2.2 Josephson equations........................ 12 2.2.3 Josephson contacts......................... 13 2.2.4 DC - Josephson effect........................ 14 2.2.5 AC - Josephson effect........................ 14 2.2.6 Josephson contacts in the magnetic field............. 14 2.3 I-U Characteristics of Josephson Junctions................ 16 2.4 Radiation emission............................. 17 2.5 Point Contacts............................... 17 2.6 Layer Contacts............................... 18 2.7 Summary of fundamental terms...................... 18 3 Experimental Setup 20 3.1 Sample.................................... 20 3.2 Sample Holder................................ 20 3.3 Measurement Equipment.......................... 22 4 Measurement 26 4.1 Cooling down the sample rod....................... 26 4.2 Measuring the I-U-curve.......................... 26 4.3 Measurement of the field dependent critical current........... 27 4.4 Warming up the sample rod........................ 28 2 CONTENTS 3 5 Exercises 29 5.1 Questions.................................. 29 5.2 Evaluation.................................. 29 5.2.1 Introduction............................. 29 5.2.2 Zero field measurement....................... 30 5.2.3 Field dependent measurements.................. 30 Chapter 1 Safety This experiments includes operating a low-temperature cryostat and the handling of cryogenic liquids, in particular liquid helium. The latter has a boiling point of 4:2 K and thus, when exposed to skin, can cause severe cold burn and frost bite. Furthermore, if larger quantities of liquid helium are spilled, the gaseous helium can replace the oxygen in the laboratory and cause hereby asphyxiation. The tutor will give a safety briefing covering a risk assessment of the experiments and the proper use of the safety equipment. Handling of the equipment is only permitted in attendance of or after consulting the tutor! 1.1 Handling of liquid helium General At the Walther-Meißner-Institut liquid helium is operated in a closed cycle system. Helium dewars { the storage and transport vessels for liquid helium { must be connected to the return line as otherwise pressure will build up in the vessel. Nevertheless, dewars are designed to provide means of transportation for liquid cryogens and therefore transport within the building is permitted. Tilting and tipping the dewar has to be prevented at all times, as in this case the liquid helium gets in contact with "hot" parts of the dewar resulting in a quick pressure build-up and emergency gas relief. The transport of liquid cryogens in the elevator is permitted only without accompanying persons. Dangers The work with liquid helium and equipment in touch with cryogens requires special safety measurements. When operating equipment which is or was cooled by liquid or gaseous (cold) helium or removing equipment from cryostats/dewars, please keep in mind that this equipment is cold. In particular, direct skin contact will cause severe cold burns and frost bites requiring medical treatment. The same holds true for the 4 1. Safety 5 exposure of skin to cold gas or the cryogenic liquid itself. There's also the danger of asphyxiation if large quantities of liquid/gas are relieved from the dewar or cryostat (lack of oxygen). In the case of uncontrolled escape of helium the room has to be evacuated immediately. Safety measures • Always wear personal protective gear while working with the helium dewar, i.e. special (blue) cryogen gloves and safety goggles. • Keep the door to the lab open to ensure oxygen flow in the room. • Check that the helium dewar is positioned upright on an even surface. • Ensure that the helium is connected to the return line. Exceptions are during helium transfer and transport of the dewar. • When you insert or remove the dipstick into the dewar ensure to do so in a controlled and slow manner. For this please check the optimum adjustment of the clamp. Dangers: Abrupt lowering may lead to a quick evaporation of large quantities of helium and thus might result in an emergency gas relief (danger of asphyxiation). This could lead to breakdown of the insulation vacuum (resulting in even larger quantities of gas). 1.2 Electronic measurement equipment For your measurements you will use electronic equipment which is powered through the 230 V mains. I.e. inside all electronics 230 V are present. Thus all electronic appliances must be kept closed and no covers/chassis may be removed at any time. Additionally, the device and electronics used for your experiment are highly sensitive and thus laying out the measurement circuit and setting it up must be discussed with the tutor. Reconnecting/changing the wiring of the setup must be consulted and approved by the tutor { she/he must be present in the lab for this task. Dangers Physical contact with the mains supply of 230 V may be lethal! Therefore, any modi- fications to the equipment is forbidden. You must not open any pieces of equipment. Modifications to the setup are only to be done by the tutor. The assembly of the signal lines can be changed without danger. Any problems with the equipment have to be reported to the tutor imme- diately. Further information concerning safety can be found in the "red folder" in the labora- tory. 6 1. Safety 1.3 Food and drinks It is not allowed to consume food and beverages in the lab. If you need a break and want to eat or drink something,please do so outside of the lab. Please, be reminded about your personal hygiene, such as washing you hands prior to consuming foods and drinks. If you want to take a longer break, please tell the tutor. Chapter 2 Introduction 2.1 Superconductivity Superconductivity is a thermodynamic state of the solid state which is entered when the body is cooled below a critical temperature Tc. The two most prominent features of the superconducting phase are the repelling of magnetic fields out of the body and the existence of a zero-resistance state. The latter was first discovered by Heike Kamerlingh Onnes in 1911 at Leiden when the metal mercury revealed a state of infinite conductivity below the temperature of liquid helium [1]. Figure 2.1 shows the resistance values of mercury as function of temperature around the critical temperature Tc. This resistance behavior was entirely unexpected at that time as it was thought that the conductivity of metals will vanish at low temperatures. The argument was that the kinetic energy of the electrons will tend towards zero for zero temperatures. Thus, it was expected that the metal will enter a high resistance or insulation state. Exactly the opposite result was observed: the conductivity increased during the cooling process and suddenly jumped to infinity at 4:2 K corresponding to vanishing or zero electrical resistivity. It took two more decades to theoretically explain this phenomenon on a microscopic level [3,4]. Electrical conductivity in a solid is mediated by charge carriers, usually electrons. In an ordered crystal charge carrier motion is described with the Bloch model. In this quantum mechanical model electrons are described as wavefunctions. Up to this point the resistance is not included in this model. This changes, when scattering centers such as crystal imperfections or defects, lattice distortions called vibrations or phonons, or higher order effects such as electron-electron interaction comes into play. Nevertheless, superconductivity is incompatible with this description as the phenomenon was also experimentally observed in disordered and imperfect solids at finite temperatures. The superconducting state is a property of the electron system, where the electrons are able to move non-dissipatively, similar to electrons in atomic orbitals or molecules. Furthermore, spectrally resolved absorption experiments in the far infrared regime indicate that superconductors have an energy gap. Additionally, long range order in the 7 8 2. Introduction 0.15 Hg 0.12 0.09 ) Ω ( R 0.06 0.03 10-5 Ω 0.00 4.0 4.1 4.2 4.3 4.4 T (K) Figure 2.1: Superconductivity in mercury. Below T = 4:2 K the mercury has a van- ishing resistance. The data shown is taken from the original publication of Onnes (cf. Ref. [1]). The data graph is taken from [2]. 2. Introduction 9 conduction electron system is observed. A complete explanation for these observations started with the suggestion by Fr¨ohlich that an attractive interaction between the electrons mediated by phonons might give rise to a superconducting state. This idea was taken up by Cooper [5{7] and eventually lead to the formulation for the BCS theory for superconductivity [3,4]. The key idea is that electrons form pairs in the phase space, so-called Cooper pairs. The momentum state of these pairs can be thought of two electrons with opposing momenta and spin states jpi "; −pi #i. If one of the electrons is scattered that second one can compensate for this scattering event. Thus, when exposed to an external force, e.g. an electric field, j(pi + P=2) "; (−pi + P=2) #i, where P is the momentum of the cooper pair. Here, in P, contrary to the single electron case, no momentum distribution is present. Thus, the entire ensemble of Cooper pairs moves with momentum P allowing to summarize the behavior of these quasi particles with a macroscopic wavefunction ΨP = Ψ exp (i φ(r)) (2.1) with φ(r) = P · r=h¯. Therefore, the whole superconductor appears to the electrons as a (giant) molecule in which the wave packets move with a stable phase relation. In a current-free state, this phase is a constant in space.